This is entirely a driver thing. Any triangle that goes outside of the range is automatically handled by your driver, in theory by subdividing the triangle into two smaller ones; I doubt you will be able to do it faster than your GPU.
There are techniques used to optimize the triangles outside the drawing range without subdivision, though; you might specify a zone that won't need subdivision (sort of a border), and if the point happens to lie inside, special processing is issued, but in general it skips the unnecessary fragment computations.
TL;DR: trust your GPU on that.